223Boundary conditions are developed for rapid granular flows in which the rheology is dominated by grain-grain collisions. These conditions are v 0 = constdv 0 fdy and u 0 = constdu 0 /dy, where v and u are the thermal (fluctuation) and flow velocities respectively, and the subscript indicates that these quantities and their derivatives are to be evaluated at the wall. These boundary conditions are derived from the nature of individual grain-wall collisions, so that the proportionality constants involve the appropriate coefficient of restitution ew for the thermal velocity equation, and the fraction of diffuse (i.e. non-specular) collisions in the case of the flow-velocity equation. Direct application of these boundary conditions to the problem of Couette-flow shows that as long as the channel width h is very large compared with a grain diameter d it is permissible to set v = 0 at the wall and to adopt the no-slip condition. Exceptions occur where dfh is not very small, when the wall is not rough, and when the grain-wall collisions are very elastic. Similar insight into other flows can be obtained qualitatively by a dimensional analysis treatment of the boundary conditions. Finally, the more difficult problem of self-bounding fluids is discussed qualitatively.

Earth's tropical and subtropical rainbands, such as Intertropical Convergence Zones (ITCZs) and monsoons, are complex systems, governed by both large-scale constraints on the atmospheric general circulation and regional interactions with continents and orography, and coupled to the ocean. Monsoons have historically been considered as regional large-scale sea breeze circulations, driven by land-sea contrast. More recently, a perspective has emerged of a global monsoon, a global-scale solstitial mode that dominates the annual variation of tropical and subtropical precipitation. This results from the seasonal variation of the global tropical atmospheric overturning and migration of the associated convergence zone. Regional subsystems are embedded in this global monsoon, localized by surface boundary conditions. Parallel with this, much theoretical progress has been made on the fundamental dynamics of the seasonal Hadley cells and convergence zones via the use of hierarchical modeling approaches, including aquaplanets. Here we review the theoretical progress made and explore the extent to which these advances can help synthesize theory with observations to better understand differing characteristics of regional monsoons and their responses to certain forcings. After summarizing the dynamical and energetic balances that distinguish an ITCZ from a monsoon, we show that this theoretical framework provides strong support for the migrating convergence zone picture and allows constraints on the circulation to be identified via the momentum and energy budgets. Limitations of current theories are discussed, including the need for a better understanding of the influence of zonal asymmetries and transients on the large-scale tropical circulation. Plain Language Summary The monsoons are the moist summer circulations that provide most of the annual rainfall to many countries in the tropics and subtropics, influencing over one third of the world's population. Monsoons in different regions have historically been viewed as separate continent-scale "sea breezes," where land heats faster than ocean in the summer, causing warm air to rise over the continent and moist air to be drawn over land from the ocean. Here we show that recent theoretical advances and observational analyses support a novel view of monsoons as localized seasonal migrations of the tropical convergence zone: the band of converging air and rainfall in the tropics embedded within the tropical atmospheric overturning circulation. This updated perspective distinguishes the dynamics of low-latitude (∼0-10°poleward) "Intertropical Convergence Zones" (ITCZs) from that of monsoons (∼10-25°poleward), explains commonalities and differences in behavior between the regional ITCZs and monsoons, and may help to understand year-to-year variability in these systems and how the global monsoon might change in the future. We end by discussing features that are not yet included in this new picture: the influence of mountains and continent shapes on the circulation and the relationship...

Theoretical understanding of the dynamics of Hadley cells, monsoons and ITCZs 9 is developing rapidly 10 • Some aspects of observed monsoons and their variability can now be understood 11 through theory 12 • Parallel theories should be reconciled and extended to account for zonal asymme-13 tries and transients 14

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Recent studies have shown that the rapid onset of the monsoon can be interpreted as a switch in the tropical circulation, which can occur even in the absence of land-sea contrast, from a dynamical regime controlled by eddy momentum fluxes to a monsoon regime more directly controlled by energetic constraints. Here we investigate how one aspect of continental geometry, that is the position of the equatorward coastal boundary, influences such transitions. Experiments are conducted with an aquaplanet model with a slab ocean, in which different zonally symmetric continents are prescribed in the Northern Hemisphere poleward from southern boundaries at various latitudes, with “land” having a mixed layer depth two orders of magnitude smaller than ocean. For continents extending to tropical latitudes, the simulated monsoon features a rapid migration of the convergence zone over the continent, similar to what is seen in observed monsoons. For continents with more poleward southern boundaries, the main precipitation zone remains over the ocean, moving gradually into the summer hemisphere. We show that the absence of land at tropical latitudes prevents the rapid displacement into the subtropics of the maximum in lower-level moist static energy and, with it, the establishment of an overturning circulation with a subtropical convergence zone that can transition rapidly into an angular momentum conserving monsoon regime.